Theta functions in differential and arithmetic geometry

微分几何和算术几何中的 Theta 函数

• 批准号: RGPIN-2017-04959
• 负责人: Sankaran, Siddarth
• 金额: $ 1.53万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635476
• 关键词: Theta; functions; differential; arithmetic; geometry

My research lies in the field of arithmetic geometry, at the interface of two mathematical subfields: number theory and geometry. Number theory is the study of integers, which are essentially discrete and rigid in nature. On the other hand, geometry deals with objects that are continuous, that can be stretched and pulled and deformed in a fluid manner. Arithmetic geometry marries these two points of view, applying tools and intuitions from the world of geometry to gain greater insight into number theoretic phenomena, and vice versa.

我的研究在于两个数学子场的界面：数字理论和几何形状的界面。数字理论是整数的研究，本质上是离散和僵化的。另一方面，几何形状涉及连续的物体，这些物体可以以流畅的方式拉伸，拉动和变形。算术几何形状结合了这两种观点，应用了几何世界的工具和直觉，以更深入地了解数量的理论现象，反之亦然。